First Advisor

Jay Gopalakrishnan

Term of Graduation

Spring 2021

Date of Publication


Document Type


Degree Name

Doctor of Philosophy (Ph.D.) in Mathematical Sciences


Mathematics and Statistics



Physical Description

1 online resource (xix, 148 pages)


In this dissertation we present a simplified scalar numerical model, derived from Maxwell's field equations, for the fiber laser amplifier simulations. Maxwell's equations are reduced using a technique called Coupled Mode Theory (CMT).

The reduced model is made more efficient through a new scale model, referred to as an equivalent short fiber, which captures some of the essential characteristics of a longer fiber. The equivalent short fiber can be viewed as a fiber made using artificial (nonphysical) material properties that in some sense compensates for its reduced length. The computations can be accelerated by a factor approximately equal to the ratio of the original length to the reduced length of the equivalent fiber. Computations using models of two commercially available fibers – one doped with ytterbium, and the other with thulium-show the practical utility of the concept. Extensive numerical studies are conducted to assess when the equivalent short fiber model is useful and when it is not.

Fiber quantum defect heating is included in the model. We solve the heat equation coupled with our CMT equation to get the solution. Transverse Mode Instability (TMI) is observed in both ytterbium and thulium doped fibers. Various power thresholds are presented for TMI. Also, to find the root cause of TMI and to investigate how to mitigate this chaotic process, we have experimented with different refractive index gratings. A few gratings are presented with numerical results which show promises.

Finally this dissertation uses numerical simulations of a thulium-doped optical fiber amplifier to predict various performance characteristics such as peak temperatures, expected output powers and efficiencies, presence of Amplified Spontaneous Emission (ASE), et cetera. Single- and two-tone configurations are studied. In the latter case, the two laser sources are separated in frequency by the amount that corresponds to the peak Raman gain, and a few seed ratios at various total seed powers are examined.

To reduce the excessive computational time and resources needed to simulate the CMT equations and also to study TMI efficiently after sufficient number of time-steps, the code is parallelized using both shared and distributed memory configurations. The techniques employed in this strategy give linear speedup as we increase the number of time-steps for a fixed number of nodes.


© 2021 Tathagata Goswami

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